Question

(1 point) The problem below describes an experiment and defines a random variable. For this problem:
(a) Find the distribution of the random variable (and provide it as a chart).
(b) Calculate the expected value of the random variable.

Roll two fair, six-sided dice. Let X be the (absolute value of the) difference between the numbers they will land on.

a. The distribution of the random variable (enter possible values in numerical order):

xx
P(x)P(x)

b. The expected value of the random variable:

The problem below describes an experiment and defines a random variable. For this problem:
(a) Find the distribution of the random variable (and provide it as a chart).
(b) Calculate the expected value of the random variable.

A room has 15 art majors and 10 science majors. Two students are selected randomly (without replacement). Let S be the number of science majors that will be drawn.

a. The distribution of the random variable (put possible values in numerical order):

ss
P(s)P(s)

b. The expected value of the random variable:

2.

(1 point)
A large class with 1,000 students took a quiz consisting of ten questions. To get an A, students needed to get 9 or 10 questions right. To pass, students needed to get at least 6 questions right.
Let X be the number of questions a student got right. The distribution of X is given below.

xP(x)00.0410.0720.0930.1440.1650.0460.0870.1280.1590.06100.05x012345678910P(x)0.040.070.090.140.160.040.080.120.150.060.05

a) If a student is selected randomly from the class, what is the probability he got an A on the quiz?



b) How many students got an A on the quiz?



c) How many students did not miss a single question on the quiz?



d) If a student is selected randomly from the class, what is the probability he passed the quiz?



e) How many students passed the quiz?



f) How many students failed the quiz?



g) If a student is selected randomly from the class, what is the probability that student got at least one question right?

Answer 1